Collect all five hidden Tori birds found in the following songs by pressing Y: World 1-4, World 2-6, World 3-7, World 5-8 (unlocked after completing the game), and World 7-3. To locate them, search for a "cloud" portion on the ground. At the end of that portion you will find an egg. Hit it to get the Tori bird. Get all the Tori birds, then return to Symphony City and unlock the door near the city to access Sky Roost.
In order to open up the "Fast Mode" for each stage, first earn enough notes to get a golden blossom. This unlocks the Fast Mode for the stage: you press Y, then navigate to the desired stage in that menu, then press X to play in this fast-paced mode. If you get another golden blossom on the Fast Mode playthrough, you can get a special image - every stage has it's own unique image.